d/(dt)((x)(t+sin(t)-1))

解答

\frac{d}{d t} ((x) (t + sin (t) - 1))

\frac{d x}{d t} (t + sin (t) - 1) + (cos (t) + 1) x

求解步骤

\frac{d}{d t} ((x) (t + sin (t) - 1))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = t + sin (t) - 1

= \frac{d x}{d t} (t + sin (t) - 1) + \frac{d}{d t} (t + sin (t) - 1) x

\frac{d}{d t} (t + sin (t) - 1) = cos (t) + 1

= \frac{d x}{d t} (t + sin (t) - 1) + (cos (t) + 1) x

e x p an d \frac{4 ( s + 2 )}{( s + 1 ) ( s + 3 )}

e x p an d (a e^{3} - 2 a^{2} + 4) (a e^{3} - 3 a)

e x p an d \frac{2}{( 4 + h ) ^{2}}

e x p an d (a - 2, b - 2) (\frac{b}{a})^{3}

e x p an d 3 \cdot 10.2